We have observed the orbital ordering in the ferromagnetic Mott-insulator Lu2V2O7 by the polarized neutron diffraction technique. The orbital ordering pattern determined from the observed magnetic form factors can be explained in terms of a linear combination of wave functions |yz>, |zx> and |xy>; |0> = (1/3)^(1/2) |xy> + (1/3)^(1/2)|yz> + (1/3)^(1/2) |zx> which is proportional to |(x + y + z)^2 - r^2>; where each orbital is extended toward the center-of-mass of the V tetrahedron. We discuss the stability of the ferromagnetic Lu2V2O7, using a Hubbard Hamiltonian with these three orbitals.
A lightly doped perovskite mangantite La_{0.88}Sr_{0.12}MnO_3 exhibits a phase transition at T_{OO}=145 K from a ferromagnetic metal (T_C=172 K) to a novel ferromagnetic insulator.We identify that the key parameter in the transition is the orbital degree of freedom in e_g electrons. By utilizing the resonant x-ray scattering technique, orbital ordering is directly detected below T_{OO}, in spite of a significant diminution of the cooperative Jahn-Teller distortion. The new experimental features are well described by a theory treating the orbital degree of freedom under strong electron correlation. The present experimental and theoretical studies uncover a crucial role of the orbital degree in the metal-insulator transition in lightly doped manganites.
We present powder and single crystal X-ray diffraction data as evidence for a monoclinic distortion in the low spin (S=0) and intermediate spin state (S=1) of LaCoO3. The alternation of short and long bonds in the ab plane indicates the presence of eg orbital ordering induced by a cooperative Jahn-Teller distortion. We observe an increase of the Jahn-Teller distortion with temperature in agreement with a thermally activated behavior of the Co3+ ions from a low-spin ground state to an intermediate-spin excited state.
Orbital-ordering instability arising due to the intrapocket nesting is investigated for the tight-binding models of pnictides in the presence of orbital-lattice coupling. The incommensurate instabilities with small momentum, which may play an important role in the nematic-ordering transition, vary from model to model besides being more favorable in comparison to the spin-density wave instability in the absence of good interpocket nesting. We also examine the doping dependence of such instabilities. The electron-phonon coupling parameter required to induce them are compared with the first-principle calculations.
Using first principle band structure calculations, we critically examine results of resonant x-ray scattering experiments which is believed to directly probe charge and orbital ordering. Considering the specific case of La0.5Sr1.5MnO4, we show that this technique actually probes most directly and sensitively small structural distortions in the system. Such distortions, often difficult to detect with more conventional techniques, invariably accompany and usually cause the orbital and charge orderings. In this sense, this technique is only an indirect probe of such types of ordering. Our results also provide a microscopic explanation of the novel types of charge and orbital ordering realized in this system and other doped manganites.
We consider the superexchange in `frustrated Jahn-Teller systems, such as the transition metal oxides NaNiO_2, LiNiO_2, and ZnMn_2O_4, in which transition metal ions with doubly degenerate orbitals form a triangular or pyrochlore lattice and are connected by the 90-degree metal-oxygen-metal bonds. We show that this interaction is much different from a more familiar exchange in systems with the 180-degree bonds, e.g. perovskites. In contrast to the strong interplay between the orbital and spin degrees of freedom in perovskites, in the 90-degree exchange systems spins and orbitals are decoupled: the spin exchange is much weaker than the orbital one and it is ferromagnetic for all orbital states. Due to frustration, the mean-field orbital ground state is strongly degenerate. Quantum orbital fluctuations select particular ferro-orbital states, such as the one observed in NaNiO_2. We also discuss why LiNiO_2 may still behave as an orbital liquid.